My god, people are so needlessly vile to men who post looking for genuine advice on this site. If it was a woman posting about her husband's lack of interest in sex, she'd get a completely different response.
OP, first of all, your wife sounds very, very anxious if she won't go out unless there is a potential backup childcare in case something goes wrong with the actual childcare. Has she seen a doctor about her anxiety? Because it sounds way beyond normal worrying.
Secondly, what reasons has your wife given in the past for not wanting sex? Does she literally just not have any sex drive at all, or is there some anxiety or barrier that's stopping her from doing it? For example, does she fear getting pregnant again?
Thirdly, is she using hormonal birth control of some kind? In particular, is she on a progestogen-only method like a hormonal IUD, implant or progestogen-only pill? I only ask that question because when I was using a specific type of birth control, my sex drive absolutely withered and died completely (I mean, you can't say it wasn't an effective birth control method, I suppose) and it was only when I stopped taking it that my sex drive returned.